Fractions: Equivalent Ratios, Mixed Numbers, and Operations

Equivalent Ratios

• Two fractions are equivalent if they have the same value
• Can be obtained by multiplying or dividing both numerator and denominator by the same number
• Example: 1/2 is equivalent to 2/4 or 3/6
• To find an equivalent ratio, multiply or divide both numerator and denominator by the same number

Converting Mixed Numbers

• A mixed number is a combination of a whole number and a proper fraction
• Can be converted to an improper fraction by multiplying the whole number part by the denominator and adding the numerator
• Example: 2 3/4 = (2 x 4) + 3 = 11/4
• Can be converted back to a mixed number by dividing the numerator by the denominator and finding the remainder

Like and Unlike Denominators

• Like denominators: fractions with the same denominator
• Can be added or subtracted by adding or subtracting the numerators and keeping the same denominator
• Example: 1/4 + 2/4 = 3/4
• Unlike denominators: fractions with different denominators
• Need to find the least common multiple (LCM) of the denominators to add or subtract
• Example: 1/4 + 1/6 = find LCM of 4 and 6, which is 12, then convert both fractions to have a denominator of 12: 3/12 + 2/12 = 5/12

Real-world Applications

• Measuring ingredients for cooking or baking
• Measuring distances or lengths in construction or carpentry
• Comparing proportions of different quantities
• Solving problems involving parts of a whole, such as dividing a pizza or a cake
• Real-world examples help to illustrate the importance of adding and subtracting fractions with like and unlike denominators